Propagation of Waves

When a wave propagates from one medium to another with different densities, part of it gets reflected back into the first medium and part gets transmitted into the second medium. The wave speed differs between media—it travels slower in denser media and faster in rarer media. Both reflected and transmitted waves have reduced amplitudes compared to the incident wave.

Phase behavior depends on the direction of propagation. When a wave travels from a denser to a rarer medium, both reflected and transmitted waves remain in phase with the incident wave. Conversely, when traveling from a rarer to a denser medium, the reflected wave is 180° out of phase with the incident wave, while the transmitted wave stays in phase.

The refractive index is a quantity that compares the velocity of electromagnetic waves in different media. It is expressed as the ratio of the velocity of light in a vacuum to the velocity of light in a given medium. This index helps explain why wave propagation velocity varies between materials of different densities.

Wave speed depends on the linear mass density of the medium. When tension is constant, a string with higher linear mass density has a lower wave speed than a string with lower linear mass density. This relationship explains why waves propagate at different rates through materials with varying densities.

Both the reflected and transmitted waves have amplitudes smaller than the incident wave's amplitude. This amplitude reduction occurs regardless of whether the wave travels from a denser to a rarer medium or vice versa. The energy is distributed between reflection and transmission at the boundary.

The interface between two media acts as a boundary that is neither fixed nor free. At this boundary, the incident wave splits into reflected and transmitted components. The properties of each medium—particularly their density and linear mass density—determine how much energy reflects versus transmits across the interface.

When tension is equal in both strings, the wave speed depends solely on linear mass density. A wave traveling from high to low linear mass density experiences different reflection and transmission characteristics than one traveling the opposite direction. Equal tension ensures that density differences alone determine wave speed and phase relationships.